We saw that, in consequence of gravitation, the Einsteinian universe is not Euclidean, but curved. It is, as we said, difficult, if not impossible, to visualise a curvature of space. But the difficulty exists only for our imagination, which is restricted by our life of sense, not for our reason, which goes farther and higher. It is one of the commonest of errors to suppose that the wings of the imagination are more powerful than those of reason. If one wants proof of the contrary, one has only to compare what the most poetic of ancient thinkers made of the starry heavens with what modern science tells about the universe. Here is the way to approach our problem. Let us not notice for the moment the rather irregular distribution of stars in our stellar system, and take it as fairly homogeneous. What is the condition required for this distribution of the stars under the influence of gravitation to remain stable? Calculation gives us this reply: The curvature of space must be constant, and such that space is bent like a spherical surface. Rays of light from the stars may travel eternally, indefinitely, round this unlimited, yet finite, universe. If the cosmos is spherical in this way, we can even imagine the rays which emanate from a star—the sun, for instance—crossing the universe and converging at the diametrically opposite point of it. In such case we might expect to see stars at opposite points in the heavens, of which one would be the image, the spectre, the “double” of the other—in the sense which the ancient Egyptians gave to the word. Properly speaking, this “double” would represent, not the generating star as it is, but as it was at the time when it emitted the rays which form the double, or millions of years earlier. If we observe the original and the double star, the reality and the mirage, simultaneously from some remote part of the stellar system, such as our planet, we shall see a great difference between them, since the “copy” will show us the original as it was thousands of centuries before. It may, in fact, happen that the second star is more brilliant than the first, because in the meantime the first has gradually cooled, and may even be extinct. * * * * * It is improbable that we should find many of these phantom-stars, or virtual stars, luminous and unreal daughters of heavy suns. The reason is that the rays in their passage through the universe will generally be diverted by the stars near which they pass. Concentration or convergence of them at the antipodes of the real star must be rare. Moreover, the rays are to some extent absorbed by the cosmic stuff they meet in space. It is, however, not impossible that the astronomers of the future may discover such phenomena. It is, in fact, not impossible that we have already observed such things without knowing it.